Two spectral Legendre's derivative algorithms for Lane-Emden, Bratu equations, and singular perturbed problems
M Abdelhakem, YH Youssri - Applied Numerical Mathematics, 2021 - Elsevier
This research aims to assemble two methodical spectral Legendre's derivative algorithms to
numerically attack the Lane-Emden, Bratu's, and singularly perturbed type equations. We …
numerically attack the Lane-Emden, Bratu's, and singularly perturbed type equations. We …
A novel spectral Galerkin/Petrov–Galerkin algorithm for the multi-dimensional space–time fractional advection–diffusion–reaction equations with nonsmooth solutions
The usual classical polynomials-based spectral Galerkin and Petrov–Galerkin methods
enjoy high-order accuracy for problems with smooth solutions. However, their accuracy and …
enjoy high-order accuracy for problems with smooth solutions. However, their accuracy and …
Shifted fifth-kind Chebyshev polynomials Galerkin-based procedure for treating fractional diffusion-wave equation
AG Atta, WM Abd-Elhameed… - International Journal of …, 2022 - World Scientific
Herein, we propose new efficient spectral algorithms for handling the fractional diffusion
wave equation (FDWE) and fractional diffusion wave equation with damping (FDWED). In …
wave equation (FDWE) and fractional diffusion wave equation with damping (FDWED). In …
Convergence analysis of an L1-continuous Galerkin method for nonlinear time-space fractional Schrödinger equations
This paper develops and analyses a finite difference/spectral-Galerkin scheme for the
nonlinear fractional Schrödinger equations with Riesz space-and Caputo time-fractional …
nonlinear fractional Schrödinger equations with Riesz space-and Caputo time-fractional …
Advanced shifted sixth-kind Chebyshev tau approach for solving linear one-dimensional hyperbolic telegraph type problem
A new numerical scheme based on the tau spectral method for solving the linear hyperbolic
telegraph type equation is presented and implemented. The derivation of this scheme is …
telegraph type equation is presented and implemented. The derivation of this scheme is …
An easy to implement linearized numerical scheme for fractional reaction–diffusion equations with a prehistorical nonlinear source function
In this paper, we construct and analyze a linearized finite difference/Galerkin–Legendre
spectral scheme for the nonlinear Riesz-space and Caputo-time fractional reaction–diffusion …
spectral scheme for the nonlinear Riesz-space and Caputo-time fractional reaction–diffusion …
A spectral collocation method for solving the non-linear distributed-order fractional Bagley–Torvik differential equation
One of the issues in numerical solution analysis is the non-linear distributed-order fractional
Bagley–Torvik differential equation (DO-FBTE) with boundary and initial conditions. We …
Bagley–Torvik differential equation (DO-FBTE) with boundary and initial conditions. We …
Galerkin operational approach for multi-dimensions fractional differential equations
The current manuscript introduces a novel numerical treatment for multi-term fractional
differential equations with variable coefficients. The spectral Galerkin approach is developed …
differential equations with variable coefficients. The spectral Galerkin approach is developed …
A new efficient algorithm based on fifth-kind Chebyshev polynomials for solving multi-term variable-order time-fractional diffusion-wave equation
K Sadri, H Aminikhah - International Journal of Computer …, 2022 - Taylor & Francis
An algorithm based on a class of the Chebyshev polynomials family called the fifth-kind
Chebyshev polynomials (FCPs) is introduced to solve the multi-term variable-order time …
Chebyshev polynomials (FCPs) is introduced to solve the multi-term variable-order time …
Tanh Jacobi spectral collocation method for the numerical simulation of nonlinear Schrödinger equations on unbounded domain
We present a class of orthogonal functions on infinite domain based on Jacobi polynomials.
These functions are generated by applying a tanh transformation to Jacobi polynomials. We …
These functions are generated by applying a tanh transformation to Jacobi polynomials. We …